The interaction of cytokine and T-cells in our body keeps the regulation of immune system and helps in various biological functions [1]}. Since the cytokine production by T-cells is quite essential for developing immune system, we considered a simple of cytokines and T cells interaction, where, all possible cytokine production mechanisms are associated. We used stochastic formalism to study the model by constructing Master equation of the model system specifically considering the dynamics of cytokines. The constructed Master equation is solved analytically using generating function technique and the solved probability distribution function, which describes the pattern of distribution of dynamical cytokines in the system, is found to be quite complex. However, under certain limiting conditions, we explored few interesting patterns which carry the information of the system. Near thermodynamics limit, the probability distribution function becomes modified Poisson distribution which indicates that the distribution of the cytokines in the system exhibit classical Poisson pattern. This property indicates that the cytokine events occurring in the system is purely random and the pattern is exhibited mostly by the self-organised aggregation of spatiotemporal random cytokine events scattered over the entire system. In such situation, Poisson pattern behaves as a basin of attraction which attracts cytokine random processes towards it and nonrandom processes are away from it [2]}. The uncertainty or surprise of random cytokine events is measured by complexity measurement parameter Shannon entropy which we found to be time dependent. The information stored in the Poisson pattern is then calculated as the difference of maximum entropy and entropy at any instant of time, and found that the competition between overall production rate of cytokines and overall decay rate of it need to be balanced such that information stored in the Poisson pattern should be optimised and non-zero.
